Symbolic algebra: Sage, Maxima, Ginac, Sympy?

Hi all.
In this period I am working on symbolic matrices, and I am a bit confused about the various possibilities and the mutual relationships.

If I understand correctly, for symbolic computation Sage uses Ginac and Maxima, but I have no a clear idea of the different roles of the two packages in Sage own engine.

Furthermore, I am reading some tutorials about Sympy. I know that Sympy is included in the huge library of Sage packages, but it is not directly used in any way by Sage for symbolic computation?
Could you please clarify a bit these points?

Comments

Thanks for the clarifications and the link.
Sometimes is not easy to understand the differences and the mutual dependencies of the various mathematical package related to Sage. For this reason your answer is really helpful, I will continue to experiment with Sage and Sympy.